#include <bits/stdc++.h> using namespace std; typedef long long LL; typedef long double LD; typedef pair < int, int > PII; typedef pair < LL, LL > PLL; typedef pair < LD, LD > PDD; #define _upgrade ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); #define all(x) (x).begin(), (x).end() #define sz(x) (int)(x).size() template < typename _T > inline void _DBG(const char *s, _T x) { cerr << s << " = " << x << "\n"; } template < typename _T, typename... args > void _DBG(const char *s, _T x, args... a) { while(*s != ',') cerr << *s++; cerr << " = " << x << ','; _DBG(s + 1, a...); } #ifdef LOCAL #define DBG(...) _DBG(#__VA_ARGS__, __VA_ARGS__) #define __gcd gcd #else #define DBG(...) (__VA_ARGS__) #define cerr if(0) cout #endif // ********************** CODE ********************** // const int N = 1e3 + 7; const int K = 15; LL dp[N][K][2][2], sm[N][K][2][2], memo[N][N], p; bool vis[N][N]; LL newton(int n, int k) { if(n < k || k < 0) return 0; if(n == k || k == 0) return 1; return memo[n][k]; } int n, k; int main() { _upgrade cin >> n >> k >> p; if(k > 12) { cout << 0 << "\n"; return 0; } for(int i = 0; i <= n; i++) { for(int j = 0; j <= i; j++) { if(i == j || j == 0) memo[i][j] = 1; else { memo[i][j] = memo[i - 1][j] + memo[i - 1][j - 1]; if(memo[i][j] >= p) { memo[i][j] -= p; } } } } dp[1][0][0][0] = 1; dp[1][1][0][1] = 1; dp[1][1][1][0] = 1; dp[1][1][1][1] = 1; sm[1][1][0][0] = 1; for(int j = 1; j <= k; j++) { sm[1][j][0][0] = 1; sm[1][j][0][1] = 1; sm[1][j][1][0] = 1; sm[1][j][1][1] = 1; } for(int i = 2; i <= n; i++) { for(int j = 1; j <= k; j++) { for(int l = 0; l < 2; l++) { for(int r = 0; r < 2; r++) { if(l == 1 && r == 0) { dp[i][j][l][r] = dp[i][j][r][l]; sm[i][j][l][r] = (sm[i][j - 1][l][r] + dp[i][j][l][r]) % p; continue; } for(int s = 2; s < i; s++) { int j2 = (max(l, r) == 1 ? j - 1 : j); if(l == r) { dp[i][j][l][r] = (dp[i][j][l][r] + dp[s - 1][j2][l][1] * dp[i - s][j2][1][r] % p * newton(i - 1, s - 1)) % p; dp[i][j][l][r] = (dp[i][j][l][r] + dp[s - 1][j][l][1] * sm[i - s][j - 1][1][r] % p * newton(i - 1, s - 1)) % p; dp[i][j][l][r] = (dp[i][j][l][r] + sm[s - 1][j - 1][l][1] * dp[i - s][j][1][r] % p * newton(i - 1, s - 1)) % p; } if(l == 0 && r == 1) { dp[i][j][l][r] = (dp[i][j][l][r] + dp[s - 1][j][l][1] * sm[i - s][j - 1][1][r] % p * newton(i - 1, s - 1)) % p; dp[i][j][l][r] = (dp[i][j][l][r] + sm[s - 1][j - 1][l][1] * dp[i - s][j - 1][1][r] % p * newton(i - 1, s - 1)) % p; } } if(l == r) { dp[i][j][l][r] = (dp[i][j][l][r] + dp[i - 1][j][1][r]) % p; dp[i][j][l][r] = (dp[i][j][l][r] + dp[i - 1][j][l][1]) % p; } if(l == 0 && r == 1) { dp[i][j][l][r] = (dp[i][j][l][r] + dp[i - 1][j - 1][1][r]) % p; dp[i][j][l][r] = (dp[i][j][l][r] + dp[i - 1][j][l][1]) % p; } sm[i][j][l][r] = (sm[i][j - 1][l][r] + dp[i][j][l][r]) % p; } } } } cout << dp[n][k][0][0] << "\n"; return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 | #include <bits/stdc++.h> using namespace std; typedef long long LL; typedef long double LD; typedef pair < int, int > PII; typedef pair < LL, LL > PLL; typedef pair < LD, LD > PDD; #define _upgrade ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); #define all(x) (x).begin(), (x).end() #define sz(x) (int)(x).size() template < typename _T > inline void _DBG(const char *s, _T x) { cerr << s << " = " << x << "\n"; } template < typename _T, typename... args > void _DBG(const char *s, _T x, args... a) { while(*s != ',') cerr << *s++; cerr << " = " << x << ','; _DBG(s + 1, a...); } #ifdef LOCAL #define DBG(...) _DBG(#__VA_ARGS__, __VA_ARGS__) #define __gcd gcd #else #define DBG(...) (__VA_ARGS__) #define cerr if(0) cout #endif // ********************** CODE ********************** // const int N = 1e3 + 7; const int K = 15; LL dp[N][K][2][2], sm[N][K][2][2], memo[N][N], p; bool vis[N][N]; LL newton(int n, int k) { if(n < k || k < 0) return 0; if(n == k || k == 0) return 1; return memo[n][k]; } int n, k; int main() { _upgrade cin >> n >> k >> p; if(k > 12) { cout << 0 << "\n"; return 0; } for(int i = 0; i <= n; i++) { for(int j = 0; j <= i; j++) { if(i == j || j == 0) memo[i][j] = 1; else { memo[i][j] = memo[i - 1][j] + memo[i - 1][j - 1]; if(memo[i][j] >= p) { memo[i][j] -= p; } } } } dp[1][0][0][0] = 1; dp[1][1][0][1] = 1; dp[1][1][1][0] = 1; dp[1][1][1][1] = 1; sm[1][1][0][0] = 1; for(int j = 1; j <= k; j++) { sm[1][j][0][0] = 1; sm[1][j][0][1] = 1; sm[1][j][1][0] = 1; sm[1][j][1][1] = 1; } for(int i = 2; i <= n; i++) { for(int j = 1; j <= k; j++) { for(int l = 0; l < 2; l++) { for(int r = 0; r < 2; r++) { if(l == 1 && r == 0) { dp[i][j][l][r] = dp[i][j][r][l]; sm[i][j][l][r] = (sm[i][j - 1][l][r] + dp[i][j][l][r]) % p; continue; } for(int s = 2; s < i; s++) { int j2 = (max(l, r) == 1 ? j - 1 : j); if(l == r) { dp[i][j][l][r] = (dp[i][j][l][r] + dp[s - 1][j2][l][1] * dp[i - s][j2][1][r] % p * newton(i - 1, s - 1)) % p; dp[i][j][l][r] = (dp[i][j][l][r] + dp[s - 1][j][l][1] * sm[i - s][j - 1][1][r] % p * newton(i - 1, s - 1)) % p; dp[i][j][l][r] = (dp[i][j][l][r] + sm[s - 1][j - 1][l][1] * dp[i - s][j][1][r] % p * newton(i - 1, s - 1)) % p; } if(l == 0 && r == 1) { dp[i][j][l][r] = (dp[i][j][l][r] + dp[s - 1][j][l][1] * sm[i - s][j - 1][1][r] % p * newton(i - 1, s - 1)) % p; dp[i][j][l][r] = (dp[i][j][l][r] + sm[s - 1][j - 1][l][1] * dp[i - s][j - 1][1][r] % p * newton(i - 1, s - 1)) % p; } } if(l == r) { dp[i][j][l][r] = (dp[i][j][l][r] + dp[i - 1][j][1][r]) % p; dp[i][j][l][r] = (dp[i][j][l][r] + dp[i - 1][j][l][1]) % p; } if(l == 0 && r == 1) { dp[i][j][l][r] = (dp[i][j][l][r] + dp[i - 1][j - 1][1][r]) % p; dp[i][j][l][r] = (dp[i][j][l][r] + dp[i - 1][j][l][1]) % p; } sm[i][j][l][r] = (sm[i][j - 1][l][r] + dp[i][j][l][r]) % p; } } } } cout << dp[n][k][0][0] << "\n"; return 0; } |